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  • Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 21 maths textbook solution

Answers (1)

Answer:

Correct option (d)

Hint:

First solve the given determinant then find |A| for \Theta =0 and for

        \theta =\frac{\pi }{2},\frac{3\pi }{2},.......

Given:

Given that,

        Let\; \; A=\begin{vmatrix} 1 &sin\theta &1 \\ -sin\theta &1 &sin\theta \\ -1 &-sin\theta &1 \end{vmatrix}

W\! here\; \; 0\leq \theta \leq 2\pi

We have to find the |A|

Solution:

Here\; \; A=\begin{vmatrix} 1 &sin\theta &1 \\ -sin\theta &1 &sin\theta \\ -1 &-sin\theta &1 \end{vmatrix}

Expanding along R1, we get

        \left | A \right |=1+sin^{2}\theta -sin\theta (-sin\theta +sin\theta )+sin^{2}\theta +1

        \Rightarrow \left | A \right |=2+2sin^{2}

        \Rightarrow \left | A \right |=2(1+\theta )

Given\; that\; \; 0\leq \theta \leq 2\pi

For \theta=0

        \Rightarrow \left | A \right |=2

F\! or\; \theta =\frac{\pi }{2},\frac{3\pi }{2},.......

        \Rightarrow \left | A \right |=2(1+1)

        \Rightarrow \left | A \right |=4

Hence \left | A \right |\varepsilon [2,4]

Posted by

Gurleen Kaur

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